There are several possibilities. Certainly the battery cables could be one. Make sure ALL ends of ALL battery cables are removed, cleaned and properly reconnected.
Cables can be internally damaged. Here a ohm meter would be able to find the problem.
Frankly my money would be on the ignition lock. It may be time for a new one. This would be most likely if you have lots of keys and things on your key ring. The extra weight can damage the lock.
Finally if you have an anti-theft system (especially if it is after market) that could be the problem.